Deck 10: Two-Sample T-Test: Independent Samples Design

Question 1

An independent samples t test

A) involves determining if a sample mean differs significantly from a population mean.
B) involves a single score from each subject.
C) involves a pre- and post-test score from each subject.
D) is also called a repeated measures test.

Answer 1

B

Question 2

A t test that involves an independent samples design is also called a

A) within-samples design.
B) repeated measures design.
C) related-subjects design.
D) between-subjects design.

Answer 2

D

Question 3

The correct notation for the standard error value for an independent samples t test is __________.

A)
B)
C)
D)

Answer 3

A

Question 4

represents

A) the standard error value for a repeated measures t test.
B) the variance values for an independent samples t test.
C) the standard error value for an independent samples t test.
D) the effect size for an independent samples t test.

Question 5

The notation applies to a

A) z-test.
B) one-sample t test.
C) two-sample t test, independent samples design.
D) two-sample t-test, related samples design.

Question 6

The df value for an independent samples t-test is

A) n - 1.
B) n - 2.
C) n₁ + n₂ - 2.
D) n₁ - n₂.

Question 7

The sample sizes for an independent samples t test are n₁ = 24 and n₂ = 18. What df value should be used?

A) 42
B) 41
C) 40
D) 39

Question 8

If the sample size for both groups in an independent samples t test is n = 15, what degrees of freedom should be used?

A) 30
B) 28
C) 29
D) 14

Question 9

If df = 42, then the total number of participants in an independent samples t test was ________.

A) 43
B) 41
C) 40
D) 44

Question 10

The results section of an independent samples t test includes the statement "t(33) = -2.14." What was the total number of participants in the study?

A) 34
B) 32
C) 35
D) 31

Question 11

A nondirectional alternative hypothesis for an independent samples t test states that

A) there is no significant difference between means.
B) one mean will be higher or lower than the other mean.
C) a difference between means is due to chance.
D) a difference between means is due to treatment.

Question 12

Which of the following is a nondirectional null hypothesis for an independent samples t test?

A) H₀: μ₁ = μ₂
B) H₀: μ₁ ≠ μ₂
C) H₀: μ₁ ≤ μ₂
D) H₀: μ₁ > μ₂

Question 13

Which of the following is a directional null hypothesis for an independent samples t test?

A) H₀: μ₁ = μ₂
B) H₀: μ₁ ≤ μ₂
C) H₀: μ₁ ≠ μ₂
D) H₀: μ₁ > μ₂

Question 14

Which of the following is a directional alternative hypothesis for an independent samples t test?

A) H₁: μ₁ > μ₂
B) H₁: μ₁ ≠ μ₂
C) H₁: μ₁ ≤ μ₂
D) H₁: μ₁ = μ₂

Question 15

Which of the following is a nondirectional alternative hypothesis for an independent samples t test?

A) H₁: μ₁ = μ₂
B) H₁: μ₁ > μ₂
C) H₁: μ₁ ≠ μ₂
D) H₁: μ₁ ≥ μ₂

Question 16

If the alternative hypothesis is H₁: μ₁ > μ₂, then the null hypothesis would be _____________.

A) H₀: μ₁ = μ₂
B) H₀: μ₁ ≠ μ₂
C) H₀: μ₁ < μ₂
D) H₀: μ₁ ≤ μ₂

Question 17

If the null hypothesis is H₀: μ₁ ≤ μ₂, then the alternative hypothesis would be _____________.

A) H₁: μ₁ > μ₂
B) H₁: μ₁ ≥ μ₂
C) H₁: μ₁ = μ₂
D) H₁: μ₁ ≠ μ₂

Question 18

The null hypothesis for an independent samples t test specifies

A) no difference between population means.
B) no difference between sample means.
C) that there are significant differences between population means.
D) that there are significant differences between sample means.

Question 19

The null hypothesis for an independent samples t test specifies _________________ and the alternative hypothesis specifies _________________.

A) that sample means are not equal; no difference between sample means
B) no difference between sample means; that samples mean are not equal
C) that population means are not equal; no difference between population means
D) no difference between population means; that population means are not equal

Question 20

If α = .05 and p < .05 for a two-tailed independent samples t test, the result suggests that

A) there was no difference between means.
B) we should fail to reject H₀.
C) there was a significant difference between means.
D) both "a" and "b" are correct.

Question 21

If α = .01 and p > .01 for a two-tailed independent samples t test, then we can conclude that

A) there was no difference between means.
B) we should fail to reject H₀.
C) there was a significant difference between means.
D) both "a" and "b" are correct.

Question 22

The mean stubbornness scores for the 8 individuals in sample A was 36. The mean for sample B, consisting of 12 individuals, was 42. A two-tailed independent samples t test was conducted and t_obt = +2.33. Given an α = .05, we can conclude that

A) there was no significant difference between the means.
B) there was a significant difference between the means.
C) the null hypothesis should be rejected.
D) both "b" and "c" are correct.

Question 23

A two-tailed independent samples t test was conducted with an α = .01. The mean for group A, consisting of 8 individuals, was 63. The mean for group B, consisting of 9 individuals, was 61. If the obtained t-value was -2.63, we could conclude that

A) there was no significant difference between the means.
B) there was a significant difference between the means.
C) the null hypothesis should be rejected.
D) both "b" and "c" are correct.

Question 24

A psychologist has developed a workshop designed to increase the degree of optimism that people experience. She conducts a one-tailed independent samples t test with an α = .01 to determine if the workshop in fact improves optimism scores. Group A, consisting of 16 individuals, participated in the workshop and subsequently obtained a M₁ = 92 on an optimism assessment. Group B, consisting of 13 individuals, takes the assessment without attending the workshop and obtained a M₂ = 88. If the obtained t-value was +2.33, we could conclude that

A) the group that attended the workshop scored significantly higher on optimism than the group that didn't attend.
B) the group that attended the workshop scored higher than the group that didn't attend, but the difference between the means was not significant.
C) the null hypothesis should be rejected.
D) Both "a" and "c" above are correct.

Question 25

In a two-tailed independent samples t test, the null hypothesis specifies the difference between means values to be ________.

A) 0
B) 1
C) .01
D) .05

Question 26

If SS for group one is 32 and SS for group two is 51 and both groups are made up of 7 individuals, what is ?

A) 6.08
B) 1.76
C) 1.39
D) 2.47

Question 27

The difference between M₁ and M₂ is 12. The pooled variance is 5. Which of the following can be used to determine Cohen's d for an independent samples t test?

A) 12/5
B) 12/
C) 5/12
D) 5/

Question 28

The difference between means is 4. The pooled variance is 9. What is the value of Cohen's d for an independent samples t test?

A) 2.25
B) .44
C) .75
D) 1.33

Question 29

The following results were reported for an independent samples t test: t(21) = -2.32, p > .01. The results suggest that

A) H₀ should be rejected.
B) H₀ should fail to be rejected.
C) the results are unlikely if H₀ is true.
D) both "a" and "c" above.

Question 30

The following results were reported for an independent samples t test: t(18) = +2.15, p < .05. The results suggest that

A) H₀ should be rejected.
B) H₀ should fail to be rejected.
C) the results are unlikely if H₀ is true.
D) both "a" and "c" above.

Question 31

If our obtained t-value for an independent samples t test is -2.21 and we are using a nondirectional alternative hypothesis, which of the following t_crit value(s) will lead to the rejection of H₀?

A) +2.18
B) -2.03
C) -2.41
D) either "a" or "b" above

Question 32

Given a t_crit of -2.01 for an independent samples t test, which of the following obtained t-value will lead to the rejection of H₀?

A) +2.88
B) -2.33
C) +2.41
D) -1.98

Question 33

For an independent samples t test, the ________ the difference between the sample means, the ________ the likelihood of rejecting H₀.

A) smaller; greater
B) smaller; less
C) larger; greater
D) larger; less

Question 34

Which of the following is not one of the assumptions of the independent samples t test?

A) Independent and random selection of subjects.
B) The dependent variable can be measured on an interval or ratio scale.
C) The dependent variable is normally distributed in the population.
D) Homogeneity of variance of the independent variable in the population of interest.

Question 35

The homogeneity of variance assumption for the independent samples t test requires that

A) the population variances of the dependent variable be approximately equal.
B) the population variances of the independent variable be approximately equal.
C) the sample sizes for the two groups be equal.
D) the dependent variable be normally distributed in the population.

Question 36

Explain the difference between a one-sample t test and an independent samples t test.

Question 37

Using symbolic notation, write the null and alternative hypotheses for a two-tailed independent samples t test.

Question 38

Using symbolic notation, write the null and alternative hypotheses for a one-tailed independent samples t test for which the researcher expects the scores in condition one to be higher than the scores in condition two.

Question 39

Using symbolic notation, write the null and alternative hypotheses for a one-tailed independent samples t test for which the researcher expects the scores in condition one to be lower than the scores in condition two.

Question 40

Describe in words what the null and alternative hypotheses state for a two-tailed independent samples t test.

Question 41

A medical researcher is studying a new drug which she believes will decrease outbreaks in people who suffer from acne. She obtains two samples of acne sufferers. Group one, consisting of 8 individuals, applies a daily facial cream which contains the active ingredient. Group two, consisting of 6 individuals, applies the same facial cream except that it does not contain the active ingredient.
a. Write the symbolic notation for the null and alternative hypotheses.
b. If t_obt = -2.84 and α = .01, was there a significant effect? How do you know?

Question 42

List the assumptions of an independent samples t test.

Question 43

Define homogeneity of variance.

Question 44

What is the pooled variance if group one, made of up 9 individuals, has an SS value of 168 and group two, made up of 10 individuals, has a SS value of 201?

Question 45

Given the summary data that follow, calculate the standard error of difference between means: SS₁ = 289, n₁ = 12, SS₂ = 315, n₂ = 15.

Question 46

Given the summary data that follow, calculate t_obt:

Question 47

Using the summary values that follow, conduct an independent samples t test with an ? = .05, two-tailed: M? = 90, n? = 18, M? = 98, n? = 16, sM?-M?=3.16.

Question 48

Using the summary values that follow, conduct a one-tailed, independent samples t test with α = .05: M₁ = 22, n₁ = 8, M₂ = 25, n₂ = 9, Assume that the researcher expects scores in condition one to be lower than the scores in condition two.

Question 49

Using the summary values that follow, conduct a two-tailed independent samples t test with α = .01:

Question 50

A sleep researcher is studying the effect of sleep deprivation on cognitive abilities. In his most recent study, one group of participants was kept awake all night and another group was allowed to sleep comfortably. Both groups were subsequently given a basic math test to see how many problems could be solved within a 5-minute period of time. Scores for both groups are listed below. The researcher believes that the sleep deprived participants will solve fewer problems
.
a. Conduct an independent samples t test with α = .01.
b. Determine and interpret the effect size.